Ok, so I know all of you are going to disagree about this theory because of the obvious age issues, buttt I think that it could easily be explained. Let's say, to cover it up Dany was told she was born in 284AC during the storm. I might be completely and absolutely wrong.
So let's pretend that this theory has merit. GRRM told Alfie Allen that Jon's story resembles that of Luke Skywalker. For those that are not familiar with Luke's story, to sum it up, Luke and Leia were attracted to each other then they found out they were twins and their father was Darth Vader. So how could Jon's story be similar to Luke's? 1- He could have a twin sister 2- His father could be alive and he's evil. It fits really well since Luke actually lived with his uncle who kept the secret of his father hidden. I don't know about Rhaegar being alive, but I think Dany and Jon could actually be twins.
So let's say that Lyanna gave birth to twins in the Tower of Joy. Ned Carried both children with him to Starfall. He left Dany there because he couldn't come back home with her since she has the Targaryen look and that's how Dany would remember the lemon trees in her childhood seeing as there are no lemon trees in Braavos and plenty in Dorne.
Another thing I noticed was that Ned thought a whole lot about the incident at the Tower of Joy and the promise he made Lyanna after Robert ordered Varys to kill Dany. He even dreamt about blood and broken promises. Why would his promise to his sister be broken if Jon was safe. There must be something else that's troubling Ned and the only thing that completely infuriated him was the assassination of Dany. Right?
Problems with this theory:
1-The obvious reason is that Jon is a year older that Dany.
2- It is widely known that Rhaella was pregnant and gave birth to Dany on Dragonstone, but that could be a lie. Dany knows nothing of her childhood in Westeros and her only source of info is Viserys.
3- If Rhaella didn't give birth to Dany, why did she die, and how? Could she have been pregnant, but died with her baby in childbirth? That could be a great opportunity to pretend Dany was the child.
4- How did Dany end up with Viserys and wouldn't he remember if she wasn't his sister?
5- The dragon has three heads. This theory only gives us two. It's possible that Lyanna could have given birth to triplets, but that's just an overkill. Who knows?
6- Who helped Ned with covering up Dany's parentage? Ser Willem?
I could be completely wrong, but I'd love to hear some feedback!!